Special equipment: 2 piping bags fitted with 1/2-inch plain tips, a spinning cake stand, optional, and a large offset spatula
For the cake: Preheat the oven to 350 degrees F. Butter two 9-inch round cake pans and line the bottom of each with parchment.
Whisk together the flour, baking powder and salt in a medium bowl. Whisk the milk, vanilla, eggs and egg yolk together in another medium bowl. Beat the butter and granulated sugar in a large bowl with an electric mixer on medium-high until light and fluffy, about 3 minutes. Add about a third of the flour mixture and beat on medium-low until incorporated. Now add a third of the egg-milk mixture and continue to beat on medium-low until incorporated, scraping down the sides of the bowl as needed. Repeat with another third of the flour, then all of the egg-milk mixture and finishing with the flour.
Divide the batter evenly between the prepared cake pans and bake until the cake has a nice golden brown crust around the edge, bounces back when pressed and a toothpick inserted in the center comes out clean, 35 to 40 minutes. Let cool completely in the cake pans on a rack.
For the frosting: Combine the confectioners' sugar, butter, milk and vanilla in a large bowl and beat with an electric mixer on low speed until all the sugar is blended into the butter. Increase the speed to medium-high and beat until light and fluffy, about 3 minutes.
Remove 3 tablespoons frosting and place it in a small bowl; leave this frosting plain. Remove another 3/4 cup frosting, place in another bowl and dye with the orange food coloring. Dye the remaining 3 3/4 cups frosting in the mixing bowl with the yellow food coloring. Fill a piping bag fitted with a 1/2-inch plain tip with the yellow frosting. Fill a second piping bag fitted with a tip with the orange frosting.
Assemble the cake: Cut a 4-inch circle out of the center of one cake layer (reserve or discard the cut-out cake). Put the cake ring on a spinning cake stand or serving platter and frost the top with about 1/2 cup of the yellow frosting. Fill the hole with the candy corn. Put the other cake layer on top, so that the rounded side of the cake is facing up; push down gently to sandwich the two cake layers together.
Pipe a ring of yellow frosting along the outside edge of the cake. Pipe a second ring just inside it so they are touching. Pipe the remaining yellow frosting onto the sides of the cake, making sure to connect it to the frosting ring on the top of the cake. Using a large offset spatula, flatten the icing on the side of the cake to frost the outside until smooth.
Pipe 3 concentric touching rings of orange frosting just inside the yellow rings. Spoon the reserved white frosting on the center of the cake and spread it flat so that it touches the orange frosting.
Position the tip of a large offset spatula in the center of the cake so the length of the blade looks like a radius and touches the top of all three frostings. Using one continuous, circular motion with gentle pressure (using a spinning cake stand will help), spread the frostings flat on the top of the cake so they form stripes (some of the frosting will come off with the spatula; do not try to reapply it). Let the cake stand at room temperature for 1 hour before serving.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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